How to Calculate Distance Between Two Angled Lines & Radius
Two lines that meet on the circumference or at the center of a circle will diverge to cut the circumference of the circle at two points. The shortest distance between these two points of intersection with the circumference is called the minor arc. Because the minor arc follows a curved path, you cannot use linear measurement tools such as rulers to measure the length of the arc. Fortunately, a relationship exists between the curved path and the radius of the circle that allows you to take advantage of simple angular and linear measurements when determining the length of curved paths.
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Instructions
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Label the two angled lines that intersect the circle with the letters A and B, and label the radius of the circle with the letter R. The radius is any straight line measured from the center to the circumference of the circle.
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Use the ruler to measure the length of the radius, R.
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Find where the lines A and B meet, and use the protractor to measure the angle (P) between the lines. If the lines meet at a point on the circumference of the circle, then the angle formed between them is an inscribed angle. If they meet at the center of the circle, then the angle between the lines is a central angle.
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Calculate the distance (S) between the two angled lines, measured along the circle circumference, in terms of the radius of the circle. If the angle between the lines is an inscribed angle, then S = (P x R x 3.142)/90. For example, for an inscribed angle of 30 degrees formed between angled lines A and B inside a circle with a radius of 1 inch, the shortest curved distance measured between A and B on the circle circumference will be S = 1.05 inches. If the angle is a central angle, then S = (P x R x 3.142)/180. For example, if lines A and B meet at the center of a circle with a radius of 1 inch and are separated by an angle of 30 degrees, the minor arc distance between A and B will be S = 0.52 inches.
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